THERMODYNAMIC AL SYSTEM OF GIBBS 93 



According to (44), the variation of the energy of the first 

 homogeneous part tlirough a change of entropy, or of volume, 

 or by a change of its mass, is 



de' = t'dt)' - v'dv' + ju/c^mi' + tii'dm^' . . . + y.n'dmn'- (62) 



We will first suppose that the components *Si, &, . . . Sn are 

 chosen so that dnii, dm^', . . . drrir! are independent and 

 express every possible variation in the composition of the 

 homogeneous mass considered. With regard to this choice of 

 components, we may note that if drrii, dnii etc. are all inde- 

 pendent, the number of components is evidently the minimum 

 by which every possible variation can be expressed. Further, 

 some of the terms in (62) may refer to substances which are not 

 present in the mass considered, but are present in other parts 

 of the system. If a component Sa is present in the homogeneous 

 mass considered, so that its quantity ma may be either increased 

 or decreased, it is termed an actual component of the given mass. 

 But if a component Sb is present in other parts of the system, but 

 not in the homogeneous mass considered, so that it is a possi- 

 bility that its quantity mb can be increased but not decreased, 

 it is termed a possible component of the given mass. 



We will first consider the case in which each of the component 

 substances Si, 82,- --Sn is an actual component of each part 

 of the system. The condition of equilibrium of the matter 

 enclosed in the envelop, since its entropy cannot vary, is that its 

 energy cannot decrease in any possible variation. Thus if 

 5e', 5e", etc. represent the change of energy of different parts of 

 the system in a variation of the state of the system, the con- 

 dition of equilibrium is 



de' + 66" + 8t"' + etc. ^ (63) [14] 



for all possible variations. Writing out the values of these 

 variations in full, we have: 



t' 8r}' — p' y + ill 8mi + H2 8m2 . . . + Mn'5m„' 

 -\-t"8r," - p"8v" + y.i"8mx" -\- ii2"8m2" . . . + iin"8mn" 

 + etc. ^ (64) [15] 



